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Quarterly Journal of Engineering Geology and Hydrogeology
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Quarterly Journal of Engineering Geology and Hydrogeology; 1982; v. 15; issue.1; p. 55-56;
DOI: 10.1144/GSL.QJEG.1982.015.01.07
© 1982 Geological Society of London

Technical Note

Least-squares fitting of the linear Mohr envelope

R. J. Lisle & C. S. Strom

Instituut voor Aardwetenschappen, Rijksuniversiteit Utrecht, , Budapestlaan 4, Postbus 80.021, 3508 TA Utrecht, Netherlands.

Introduction

Mohr's hypothesis proposes that when shear failure along a plane takes place, the normal stress {sigma} and the shear stress {tau} acting on that plane have a characteristic functional relationship. This function relating {tau} and {sigma}, it is proposed, depends on the material and can be represented on the {sigma}{tau} plane by a line defining the critical values of {alpha} and {tau} for shear failure.

In practice this critical line is constructed tangen-tially to Mohr circles representing different combinations of principal stresses applied to specimens of a particular material and is therefore referred to as the Mohr envelope.

For some materials a straight Mohr envelope with the equation {tau} = c + µ{sigma} appears from the results of triaxial testing. Furthermore in the routine testing of some materials (e.g. soils) a straight line envelope is sometimes assumed a priori. In such tests small deviations of the Mohr circles from the envelope are attributed to errors and a best-fitting straight line is used to obtain the parameters (µ, c) necessary to characterize the properties of the material.

We describe here a procedure for calculating a best-fitting straight Mohr envelope from data consisting of the applied principal stresses (i.e. from the Mohr circles).

The concept of best-fit used

The criterion used for selecting the envelope of best fit is illustrated in Fig. 1. By means of a least-squares fit we represent the Mohr envelope by a straight line {tau} = c + µ{sigma}- subject to the condition that S

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Related articles in Quarterly Journal of Engineering Geology and Hydrogeology:

Discussion on ‘Least-squares fitting of the linear Mohr envelope’ by R. J. Lisle & C. S. Strom
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Quarterly Journal of Engineering Geology and Hydrogeology 1983 16: 85. [Abstract]  



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A technique for defining non-linear shear strength envelopes, and their incorporation in a slope stability method of analysis
Quarterly Journal of Engineering Geology and Hydrogeology, 1994; 27: 231 - 241.
[Abstract] [PDF]